Homogeneous Lyapunov function for homogeneous continuous vector field
نویسنده
چکیده
The goal of this article is to provide a construction of a homogeneous Lyapunov function P associated with a system of differential equations J = f(x), x ~ R ~ (n > 1), under the hypotheses: (1) f ~ C(R n, ~ ) vanishes at x = 0 and is homogeneous; (2) the zero solution of this system is locally asymptotically stable. Moreover, the Lyapunov function V(x) tends to infinity with 1[ x [I, and belongs to C=(R~\{0}, R)n CP(~ ~, ~), with p E [~* as large as wanted. As application to the theory of homogeneous systems, we present two well known results of robustness, in a slightly extended form, and with simpler proofs.
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